List of top Structures Questions on Strain and Deformation asked in GATE AE

Consider a unit square body as shown in the figure below. The body is subjected to the deformation field \(u = -ay\) and \(v = ax\), where 'a' is a constant. Due to the application of this deformation field, the body undergoes ________ in the x-y plane.

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to __________.

 

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{30.png}
In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{30.png}
In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{30.png}

A material has Poisson's ratio \(\nu=0.5\) and Young's modulus \(E=2500\ \text{MPa}\). Under a hydrostatic stress of magnitude \(10\ \text{MPa}\), the percentage change in its volume is _________,(answer in integer).

Consider the plane strain field given by \(\varepsilon_{xx} = 10\,x y^{2}, \; \varepsilon_{yy} = -5\,x^{2}y \text{ and } \gamma_{xy} = A \, x y (2x - y)\) where \(A\) is a constant and \(\gamma_{xy}\) is the engineering shear strain. The value of \(A\) for the strain field to be compatible is .................. (rounded off to 1 decimal place).
The two-dimensional plane-stress state at a point is: \[ \sigma_{xx} = 110\,\text{MPa},\quad \sigma_{yy} = 30\,\text{MPa},\quad \tau_{xy} = 40\,\text{MPa}. \] The normal stress $\sigma_n$ on a plane inclined at $45^\circ$ as shown is (round off to the nearest integer).
An isotropic linear elastic material point under plane strain condition in the x–y plane always obeys:
The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?